Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

This paper presents the design and simulations results of a switched-capacitor discrete time Second order Sigma-Delta modulator used for a resolution of 14 bits Sigma-Delta analog to digital converter. The use of operational amplifier is necessary for low power consumption, it is designed to provide large bandwidth and moderate DC gain. With 0.35μm CMOS technology, the ΣΔ modulator achieves 86 ...

This paper presents the study of an original closed-loop conditioning approach for fully-integrated convective inertial sensors. The method is applied to an accelerometer manufactured on a standard CMOS technology using an auto-aligned bulk etching step. Using the thermal behavior of the sensor as a summing function, a first order sigma-delta modulator is built. This “electrophysical” modulator...

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–∆ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by anal...

This paper introduces a new architecture for sensor interface circuits using a delta-sigma modulator. The three-level force feedback allows the use of a digital compensator to stabilize the loop. A 3rd-order delta-sigma structure shapes the opamp noise and allows two-chip implementation with high loop gain at low frequencies.

The DC content in single-bit domain is both undesirable and hard to remove. In this paper we propose a single-bit multiplierless DC-blocker structure. The input is assumed to be sigma-delta modulated bitstream. This DC-blocker is designed using a delta modulator topology with a sigma-delta modulator (SDM) embedded in its feedback path. Its performance is investigated in terms of the overall sig...

In this paper the spectral density of the additive jitter noise in continuous time (CT) Delta-Sigma modulators (DSM) is derived analytically. Making use of the analytic results, extracted in this paper, a novel method for elimination of the damaging effects of the clock jitter in continuous time Delta-Sigma modulators is proposed. In this method instead of the conventional waveforms used in the...

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Oversampling a delta-sigma-modulated sequence, one can compute unbiased sample estimates of averages of consecutive input elements for a wide variety of inputs. We prove that these estimates are most e cient in their class (that is, variances of sample means are minimum in the class of random binary sequences gn, n = 1; : : : ; N , such that the expected values of gn are equal to the values of ...